Lusternik-schnirelmann category of spin(9)

Norio Iwase, Akira Kono

    Research output: Contribution to journalArticlepeer-review

    9 Citations (Scopus)


    First we give an upper bound of cat(E), the L-S category of a principal G-bundle E for a connected compact group G with a characteristic map α:∑V→G. Assume that there is a cone-decomposition {Fi | 0 ≤ i ≤ m} of G in the sense of Ganea that is compatible with multiplication. Then we have cat (E)≤Max(m+n, m+2) for n ≥ 1, if α is compressible into Fn ⊆ Fm ≃ G with trivial higher Hopf invariant Hn(α). Second, we introduce a new computable lower bound, Mwgt(X; F2) for cat(X). The two new estimates imply cat(Spin(9)) = Mwgt(Spin(9); F2) = 8 > 6=wgt(Spin(9); F2), where (wgt-;R) is a category weight due to Rudyak and Strom.

    Original languageEnglish
    Pages (from-to)1517-1526
    Number of pages10
    JournalTransactions of the American Mathematical Society
    Issue number4
    Publication statusPublished - Apr 2007

    All Science Journal Classification (ASJC) codes

    • Mathematics(all)
    • Applied Mathematics


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